Conditional Moments, Sub-Independence and Independence II
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Risk and Decision Analysis
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We recall a concept called sub-independence, which is defined in terms of the convolution of the distributions of random variables, providing a stronger sense of dissociation between random variables than that of uncorrelatedness. In risk and decision analysis, the investigator may encounter a stochastic model whose components are uncorrelated dependent random variables. The marginal distributions of the components are known but not their joint distribution. The investigator, however, is interested in (or in need of) the distribution of the sum of some or all of the components. The concept of sub-independence will allow the determination of the distribution of the sum of the components based on the marginal distributions of the summands. This concept is much weaker than that of independence and yet can be employed to determine the distribution of the sum of random variables from their marginal distributions. We shall mention some possible applications of the concept of sub-independence to risk and decision analysis.